Complete dissolution of spherical particles in free-fall

Abstract

A theoretical analysis is undertaken to predict the time-to-complete-dissolution (TCD) of a spherical particle in a diffusion-controlled environment. The well-known and widely-accepted mass transfer coefficient expressions of Frössling and Levich are combined with falling sphere hydrodynamics to yield simple expressions for TCD in terms of the initial particle size. These predictions compare favourably with experimental data for the disappearance of urea pellets falling in water. Asymptotic results for larger particles suggest the TCD depends linearly on initial particle size, and experiments seem to confirm this.